Packing and covering properties of sequences of convex bodies

Abstract

This paper suveys different variants of the following problem: Given a convex set $K$ and a sequence $\{C_i\}$ of convex bodies in $E^n$, is it possible to pack the sequence of bodies in $K$ or cover $K$ with the bodies? Algorithmic versions of these problems are on-line packing and on-line covering: The bodies of the sequence are given one at a time and the algorithm is to decide on the placement of the arriving body before the next body is revealed; once placed, the body cannot be moved.